Mathematical foundations Books

This book presents the main themes, techniques, and applications of geometric integrators for researchers in mathematics, physics, astronomy, and chemistry and offers a bridge from traditional training in the numerical analysis of differential equations...

This second edition presents up-to-date algorithms that are the core of all 3D computer graphics software packages. Using Core OpenGL and OpenGL ES, the book enables readers to create a complete suite of programs for 3D computer animation, modeling, and...

As MATLAB becomes nearly ubiquitous in industry and academia, it is a near necessity that professionals and students have a level of competence in its use. Until the publication of this text, however, no book had quickly and effectively introduced...

Until the authors' recent research, the practical implementation of the mathematical theory of chaos on finite machines raised several issues. This self-contained book shows how to make finite machines, such as computers, neural networks, and wireless...

This volume explores the latest research on creating algorithms and software tools to solve key combinatorial problems on large-scale high-performance computing architectures. It focuses on load balancing and parallelization on high-performance...

This book contains a systematic and formal attempt to model solutions to problems such as: Is it possible to prove a question? Is it possible to prove something by the use of questions? Do the existing paradigms in the logic of questions allow one to...

"On the Solution of Numerical Functional Equations" by Eric Harold Neville explores the methods for solving numerical functional equations, using a popular puzzle as a central example. This work offers a detailed account of the puzzle's solution,...

How can one systematically show that computer codes are correctly solving equations? Verification of Computer Codes in Computational Science and Engineering sets forth a powerful procedure called OVMSP: Order-Verification via the Manufactured Solution...

Random sets as models for set-valued observations, are a new type of data proving useful in areas such as survey sampling, biostatistics, and intelligent systems. This is the first text to explore the topic in depth, using extended probability theory to...

This book introduces advanced numerical-functional analysis to beginning computer science researchers. The reader is assumed to have had basic courses in numerical analysis, computer programming, computational linear algebra, and an introduction to real,...

Many of today's complex scientific applications now require a vast amount of computational power. General purpose graphics processing units (GPGPUs) enable researchers in a variety of fields to benefit from the computational power of all the cores...

This book corresponds to a mathematical course given in 1986/87 at the University Louis Pasteur, Strasbourg. This work is primarily intended for graduate students. The following are necessary prerequisites : a few standard...

J. Richard Biichi is well known for his work in mathematical logic and theoretical computer science. (He himself would have sharply objected to the qualifier "theoretical," because he more or less identified science and theory,...

This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it.This work is in the "public domain in the United States of America, and possibly other nations. Within the United...

This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it.This work is in the "public domain in the United States of America, and possibly other nations. Within the United...

This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it.This work is in the "public domain in the United States of America, and possibly other nations. Within the United...

This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it.This work is in the "public domain in the United States of America, and possibly other nations. Within the United...

This text unites logical and philosophical aspects of set theory in a manner intelligible to mathematicians without training in formal logic and to logicians without a mathematical background. 1961 edition.

This book includes introduction of several algorithms which are exclusively for graph based problems, namely combinatorial optimization problems, path formation problems, etc. Each chapter includes the introduction of the basic traditional nature...

Very hot area with a wide range of applications; Gives complete numerical analysis and recipes, which will enable readers to quickly apply the techniques to real problems; Includes two new techniques pioneered by Osher and...

Energy levels, resonanees, vibrations, feature extraetion, faetor analysis - the names vary from discipline to diseipline; however, all involve eigenvalue/eigenveetor eomputations. An engineer or physicist who is modeling a...

To most graph theorists there are two outstanding landmarks in the history of their subject. One is Euler's solution of the Konigsberg Bridges Problem, dated 1736, and the other is the appearance of Denes Konig's textbook in...

The finite element method (FEM) has been understood, at least in principle, for more than 50 years. The integral formulation on which it is based has been known for a longer time (thanks to the work of Galerkin, Ritz, Courant...

Since scientific software is the fuel that drives today's computers to solve a vast range of problems, huge efforts are being put into the development of new software, systems and algorithms for scientific problem solving. This...

In this book, the new and rapidly expanding field of scientific computing is understood in a double sense: as computing for scientific and engineering problems and as the science of doing such computations. Thus scientific...

As the systems which form the fabric of modern society become more complex and more interdependent, the need for the understanding of the behavior of such systems becomes increasingly more essential. What are the causes and...

The study of formal languages and of related families of automata has long been at the core of theoretical computer science. Until recently, the main reasons for this centrality were connected with the specification and analy­...

Real analytic sets in Euclidean space (Le. , sets defined locally at each point of Euclidean space by the vanishing of an analytic function) were first investigated in the 1950's by H. Cartan [Car], H. Whitney [WI-3], F. Bruhat...

Presenting basic results of topology, calculus of several variables, and approximation theory which are rarely treated in a single volume, this textbook includes several beautiful, but almost forgotten, classical theorems of Descartes, Erdős, Fejér,...

Dirk van Dalen's biography studies the fascinating life of the famous Dutch mathematician and philosopher Luitzen Egbertus Jan Brouwer. Brouwer belonged to a special class of genius; complex and often controversial and gifted...

Dirk van Dalen's popular textbook Logic and Structure, now in its fifth edition, provides a comprehensive introduction to the basics of classical and intuitionistic logic, model theory and Gödel's famous incompleteness theorem. Propositional and...

This clearly written and enlightening textbook provides a concise, introductory guide to the key mathematical concepts and techniques used by computer scientists. Topics and features: ideal for self-study, offering many pedagogical features such as...

First-Order Logic.- Model Constructions.- Properties of Model Classes.- Model Theory of Several Algebraic Theories

The author, G. J. Chaitin, shows that God plays dice not only in quantum mechanics but also in the foundations of mathematics. According to Chaitin there exist mathematical facts that are true for no reason. This fascinating...

If you have ever wondered what quaternions are - then look no further, John Vince will show you how simple and useful they are. This 2nd edition has been completely revised and includes extra detail on the invention of quaternions, a complete review of...

This revised and expanded new edition elucidates the elegance and simplicity of the fundamental theory underlying formal languages and compilation. Retaining the reader-friendly style of the 1st edition, this versatile textbook describes the essential...

The Art of Proof is designed for a one-semester or two-quarter course. A typical student will have studied calculus (perhaps also linear algebra) with reasonable success. With an artful mixture of chatty style and interesting examples, the student's...

This book introduces the main topics of modern numerical analysis: sequence of linear equations, error analysis, least squares, nonlinear systems, symmetric eigenvalue problems, three-term recursions, interpolation and...

"Proofs and Fundamentals: A First Course in Abstract Mathematics" 2nd edition is designed as a "transition" course to introduce undergraduates to the writing of rigorous mathematical proofs, and to such fundamental ...

Graph Theory.- Combinatorics.- Infinite Combinatorics and Graphs.

Preface(3rdEd).- Preface(2ndEd).- Preface(1stED).- Basic Concepts.- Sobolev Spaces.- Variational Formulation of Elliptic Boundary Value Problems.- The Construction of a Finite Element of Space.- Polynomial Approximation Theory in Sobolev Spaces.-...

This book is intended to be a thorough introduction to the subject of order and lattices, with an emphasis on the latter. It can be used for a course at the graduate or advanced undergraduate level or for independent study...

This book presents a unified theory of the Finite Element Method and the Boundary Element Method for a numerical solution of second order elliptic boundary value problems. This includes the solvability, stability, and error...

1. The ?rst edition of this book was published in 1977. The text has been well received and is still used, although it has been out of print for some time. In the intervening three decades, a lot of interesting things have happened to mathematical logic:...

Propositional Logic.- First-Order Logic.- Complete logical Calculi.- Foundations of Logic Programming.- Elements of Model Theory.- Incompleteness and Undecidability.- On the Theory of Self-Reference.

An Elementary Logic, published in 1906, is a book written by John Edward Russell. The book is a comprehensive guide to the principles of logic, aimed at beginners and students of the subject. The author introduces the basic concepts of logic, including...